Why is the wave texture not texturing these spheres?
The Rings mode of the Wave Texture node radiates from the object center in concentric shells. Because of that, the surfaces of your spheres are passing through a single shell, and therefore a single color. If you look at the edges of your images, where the distance from the center is a bit further, you can see that they are darkened:



To fix this, you can offset the location (or scale) with your mapping node:



Alternatively, if you wanted to make all the rings radiate from the same point, you could select an object in the bottom slot of the Texture Coordinate node (I chose the plane):



As a side note, the Icosphere looks pretty cool if it's scaled a bit differently: